Least Common Multiple (LCM) of 49 and 185
The least common multiple (LCM) of 49 and 185 is 9065.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 49 and 185?
First, calculate the GCD of 49 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 185 = 0 remainder 49 |
| 2 | 185 ÷ 49 = 3 remainder 38 |
| 3 | 49 ÷ 38 = 1 remainder 11 |
| 4 | 38 ÷ 11 = 3 remainder 5 |
| 5 | 11 ÷ 5 = 2 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 67 | 6834 |
| 75 and 70 | 1050 |
| 180 and 97 | 17460 |
| 182 and 187 | 34034 |
| 100 and 58 | 2900 |